Two temperature electrons (hot and cold) have been identified by the Voyager
PLS [1]} and Cassini CAPS [2]} observations in
Saturn's magnetosphere, and successively have been verified by several satellite
missions, viz., Viking Satellite [3]}, FAST Auroral Snapshot (FAST)
at the auroral region [4]} and THEMIS mission [5]},
and are governed by the super-thermal kappa/\(\kappa \) -distribution rather than
well-known Maxwellian distribution, and have also been considered by many
authors for analysing the propagation of the nonlinear electrostatic waves
[6]}, [7]}, [8]}, [9]}. The super-thermal parameter
(\(\kappa \) ) in \(\kappa \) -distribution represents super-thermality of plasma species, and
the small values of \(\kappa \)  determine the large deviation of the plasma species from
thermally equilibrium state of plasma system while for the large values of \(\kappa \) ,
the plasma system coincides with the Maxwellian distribution. Shahmansouri and Alinejad
[10]} considered three components plasma model having two temperature
super-thermal electrons and cold ions, and investigated IA solitary waves, and confirmed
that the existence of both compressive and rarefactive solitary structures in presence of
the two temperature super-thermal electrons. Baluku and Helberg theoretically and
numerically analyzed IA solitons in presence of two temperature super-thermal electrons.
Panwar et al. [6]} have demonstrated IA cnoidal waves in a three components
plasma medium having inertial cold ion and inertialess two temperature \(\kappa \) -distributed electrons,
and found that cold electron's super-thermality increases the height of the cnoidal wave.
